Predicting User Collections
Phil Henrickson
2023-06-28
What is this?
This notebook contains a set of analyses for analyzing GOBBluth89’s BoardGameGeek collection. The bulk of the analysis is focused on building a user-specific predictive model to predict the games that the specified user is likely to add to their collection.
By analyzing a user’s collection and training a predictive model, I am able to answer questions such as:
What designers/mechanics/genres does a user tend to like or dislike?
What older games might they be interested in adding to their collection?
What new and upcoming games should they check out?
1 Data
1.1 Outcomes
How many games has GOBBluth89 owned/rated/played?
1.2 Collection
What types of game does GOBBluth89 own? I can look at the most frequent types of categories, mechanics, designers, and artists that appear in a user’s collection.
1.3 Games in Collection
What games does GOBBluth89 currently have in their collection? The following table can be used to examine games the user owns, along with some helpful information for selecting the right game for a game night!
Use the filters above the table to sort/filter based on information about the game, such as year published, recommended player counts, or playing time.
2 Modeling
I’ll now the examine predictive models trained on the user’s collection.
For an individual user, I train a predictive model on their collection in order to predict whether a user owns a game. The outcome, in this case, is binary: does the user have a game listed in their collection or not? This is the setting for training a classification model, where the model aims to learn the probability that a user will add a game to their collection based on its observable features.
How does a model learn what a user is likely to own? The training process is a matter of examining historical games and finding patterns that exist between game features (designers, mechanics, playing time, etc) and games in the user’s collection.
Note: I train models to predict whether a user owns a game based only on information that could be observed about the game at its release: playing time, player count, mechanics, categories, genres, and selected designers, artists, and publishers. I do not make use of BGG community information, such as its average rating or number of user ratings (though I do use a game’s estimated complexity as a feature). This is to ensure the model can predict newly released games and is not dependent on the BGG community to rate them.
2.1 What Predicts a User’s Collection?
A predictive model gives us more than just predictions. We can also ask, what did the model learn from the data? What predicts the outcome? In the case of predicting a boardgame collection, what did the model find to be predictive of games a user owns?
To answer this, I can examine the coefficients from a model logistic regression with ridge regularization (which I will refer to as a penalized logistic regression). Positive values indicate that a feature increases a user’s probability of owning/rating a game, while negative values indicate a feature decreases the probability. To be precise, the coefficients indicate the effect of a particular feature on the log-odds of a user owning a game.
This model examines a wide variety of features of games (505 features, to be exact) and estimates their effect on whether a user owns a game. These estimates are then shrunken towards zero based on a tuning parameter (lambda), where the appropriate value is estimated from the data.
The following visualization shows the path of each feature as it enters the model, with highly influential features tending to enter the model early with large positive or negative effects.
2.2 Partial Effects
This type of model enables me to I can examine the effects of specific features on a user’s collection. For instance, what is a user’s favorite designer? Least favorite mechanic? The following plots indicate specific effects for different kinds of features.
2.3 Feature Importance
In addition to training a logistic regression, I trained another type of model using boosted trees (LightGBM), a flexible nonparametric method that is well suited for prediction.
Which features were most used by this model? Features that are important in predicting a user’s collection will appear towards the top of cover, frequency, and/or gain.
3 Assessment
How well did the model do in predicting the user’s collection?
This section contains a variety of visualizations and metrics for assessing the performance of the model(s). If you’re not particularly interested in predictive modeling, skip down further to the predictions from the model.
3.1 Separation
An easy way to examine the performance of classification model is to view a separation plot.
I plot the predicted probabilities from the model for every game (from resampling) from lowest to highest. We then overlay a blue line for any game that the user does own. A good classifier is one that is able to separate the blue (games owned by the user) from the white (games not owned by the user), with most of the blue occurring at the highest probabilities (right side of the chart).
I can more formally assess how well each model did in resampling by looking at the area under the receiver operating characteristic curve (roc_auc). A perfect model would receive a score of 1, while a model that cannot predict the outcome will default to a score of 0.5. The extent to which something is a good score depends on the setting, but generally anything in the .8 to .9 range is very good while the .7 to .8 range is perfectly acceptable.
| type | wflow_id | .metric | mean | std_err | n |
|---|---|---|---|---|---|
| resamples | glmnet | roc_auc | 0.909 | 0.018 | 5 |
| resamples | lightgbm | roc_auc | 0.884 | 0.021 | 5 |
3.2 Top Games in Training
Another way of looking at what the model learned is to see its predictions on the training set. The models are trained on games published before 2021; of these games, what did the model like for the user?
| Top (Older) Games for GOBBluth89 | |||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||
| rank | image | game | description | Pr(Own) | Own |
|---|---|---|---|---|---|
| 1 |  |
Star Wars: Rebellion (2016) | Star Wars: Rebellion is a board game of epic conflict between the Galactic Empire and Rebel Alliance for two to four players. Experience the Galactic Civil War like never before. In Rebellion, you control the entire Galactic Empire or the fledgling Rebel Alliance. You must command starships, account for troop movements, and rally systems to your cause. Given the differences between the Empire ... | 0.999 | no |
| 2 |  |
Unmatched: Little Red Riding Hood vs. Beowulf (2020) | In battle, there are no equals. ONCE UPON A TIME, Little Red Riding Hood took her basket of nasty tricks and faced off against the legendary Beowulf in this exciting Unmatched set. "What big eyes you have, Wulfie!" "That’s called 'rage', kid!" Little Red features a clever card-combo mechanism. Matching icons on the cards she plays to the one in her "basket" (discard pile), triggers potent e... | 0.966 | yes |
| 3 |  |
Unmatched: Battle of Legends, Volume Two (2021) | In battle, there are no equals. Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Batt... | 0.965 | yes |
| 4 |  |
Unmatched: Battle of Legends, Volume One (2019) | In battle, there are no equals. Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Batt... | 0.960 | yes |
| 5 |  |
A Game of Thrones: The Card Game (Second Edition) (2015) | In A Game of Thrones: The Card Game, the warring factions of Westeros await your command, inviting you to engage in a life-or-death struggle. In every game, you select devious plots and challenge your opponents on the field of battle, through back alley intrigue, and in the political arena. Whether you play a against a single opponent, in a game known as a joust, or engage in a battle of three ... | 0.955 | yes |
| 6 |  |
Concordia Venus (2018) | Concordia Venus is a standalone reimplementation of Concordia with some added features. Concordia Venus is a peaceful strategy game of economic development in Roman times for 2-6 players aged 13 and up. Instead of looking to the luck of dice or cards, players must rely on their strategic abilities. Be sure to watch your rivals to determine which goals they are pursuing and where you can outpac... | 0.953 | no |
| 7 |  |
Android: Netrunner (2012) | Welcome to New Angeles, home of the Beanstalk. From our branch offices in this monument of human achievement, NBN proudly broadcasts all your favorite media programming. We offer fully comprehensive streaming in music and threedee, news and sitcoms, classic movies and sensies. We cover it all. Ours is a brave new age, and as humanity hurtles into space and the future with an astonishing series ... | 0.949 | yes |
| 8 |  |
Unmatched: Robin Hood vs. Bigfoot (2019) | In battle, there are no equals. Unmatched is a highly asymmetrical miniature fighting game for two or four players. (Note that this set is solely for two players, but it can be combined with other sets, which all serve up to four players.) Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play exp... | 0.949 | yes |
| 9 |  |
Arkham Horror: The Card Game (Revised Edition) (2021) | The boundaries between worlds have drawn perilously thin. Dark forces work in the shadows and call upon unspeakable horrors, strange happenings are discovered all throughout the city of Arkham, Massachusetts, and behind it all an Ancient One manipulates everything from beyond the veil. It is time to revisit that which started it all… With a revamped system of organization and a number of quali... | 0.924 | no |
| 10 |  |
Bloodborne: The Board Game (2021) | Revered for its healing techniques, the town of Yharnam is rapidly degrading as a plague that turns people into beasts spreads uncontrollably. As a Hunter, it falls to you to quell this growing threat. You will have to fight through beasts, monsters, and townsfolk alike to survive the night and discover the source of this madness. In the campaign-based action-adventure Bloodborne: The Board Ga... | 0.890 | no |
I’ll plot the top 10 games most likely to be owned by the user in the last 10 years of the training set.
Games highlighted in blue are currently in the user’s collection; games highlighted in light blue are games that the user previously owned.
| Top Games by Year for GOBBluth89 | |||||||||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||||||||
| Rank | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Mage Knight Board Game | Android: Netrunner | Glass Road | Warhammer 40,000: Conquest | A Game of Thrones: The Card Game (Second Edition) | Star Wars: Rebellion | Gloomhaven | Concordia Venus | Unmatched: Battle of Legends, Volume One | Unmatched: Little Red Riding Hood vs. Beowulf | Unmatched: Battle of Legends, Volume Two |
| 2 | The Lord of the Rings: The Card Game | Star Wars: The Card Game | Impulse | Camel Up | Star Wars: X-Wing Miniatures Game – The Force Awakens Core Set | Agricola (Revised Edition) | Fallout | KeyForge: Call of the Archons | Unmatched: Robin Hood vs. Bigfoot | Unmatched: Cobble & Fog | Arkham Horror: The Card Game (Revised Edition) |
| 3 | A Game of Thrones: The Board Game (Second Edition) | Cockroach Poker Royal | Fox & Chicken | AquaSphere | Blood Rage | Star Wars: Destiny | Crossfire | Root | Tapestry | Cosmic Encounter Duel | Bloodborne: The Board Game |
| 4 | A Few Acres of Snow | Star Wars: X-Wing Miniatures Game | Circus Train (Second Edition) | Spyfall | The King Is Dead | Captain Sonar | Legend of the Five Rings: The Card Game | Cosmic Encounter: 42nd Anniversary Edition | Era: Medieval Age | Gloomhaven: Jaws of the Lion | Great Western Trail (Second Edition) |
| 5 | Mansions of Madness | The Manhattan Project | Cappuccino | Orléans | Love Letter: Adventure Time | Scythe | Carcassonne für 2 | Star Wars: X-Wing (Second Edition) | The Isle of Cats | Unmatched: Jurassic Park – InGen vs Raptors | Cascadia |
| 6 | Eclipse | Abaddon | Παλέρμο: Το Μεγάλο Ξεκαθάρισμα | Pandemic: Contagion | Love Letter: The Hobbit – The Battle of the Five Armies | Arkham Horror: The Card Game | Tau Ceti: Planetary Crisis | Newton | The Lord of the Rings: Journeys in Middle-Earth | Calico | Descent: Legends of the Dark |
| 7 | Alhambra: Family Box | Wiz-War (Eighth Edition) | Terror in Meeple City | Pandemic: The Cure | Pandemic Legacy: Season 1 | Pandemic: Iberia | Dragon Castle | Crown of Emara | Wingspan | The Fox in the Forest Duet | Boonlake |
| 8 | War of the Ring: Second Edition | Descent: Journeys in the Dark (Second Edition) | World of Tanks: Rush | Deception: Murder in Hong Kong | Star Trek: Five-Year Mission | Love Letter: Premium Edition | Pandemic Legacy: Season 2 | Azul: Stained Glass of Sintra | Nights of Fire: Battle for Budapest | Wild Space | Sheepy Time |
| 9 | Panic on Wall Street! | Axis & Allies: 1941 | Hegemonic | Port Royal | Treasure Hunter | New Angeles | Sagrada | Century: Eastern Wonders | Star Wars: Outer Rim | Trial by Trolley | Bristol 1350 |
| 10 | Ora et Labora | Terra Mystica | Room 25 | The Battle at Kemble's Cascade | Steampunk Rally | Cottage Garden | Gaia Project | Railroad Ink: Blazing Red Edition | Maracaibo | Furnace | USS Laffey: The Ship That Would Not Die |
The following table shows the model’s predictions for games in the training set.
3.3 Calibration
What do the model’s predicted probabilties mean? Or, put another way, how well calibrated are the model’s predictions?
If the model assigns a probability of 5%, how often does the outcome actually occur? A well calibrated model is one in which the predicted probabilities reflect the probabilities we would observe in the actual data. We can assess the calibration of a model by grouping its predictions into bins and assessing how often we observe the outcome versus how often each model expects to observe the outcome.
A model that is well calibrated will closely follow the dashed line - its expected probabilities match that of the observed probabilities. A model that consistently underestimates the probability of the event will be over this dashed line, be a while a model that overestimates the probability will be under the dashed line.
3.4 Validation
I first assessed the models based on their performance via resampling on the training set.
But how well does my modeling approach do in predicting new games? To test this, I assessed the performance of the model (which was trained on games published through 2021) on games published in 2022-2023.
How well did the model do? The following table shows the model’s predictions for games in the validation set.
As before, I can then assess the performance of the model.
| type | wflow_id | .metric | .estimate |
|---|---|---|---|
| valid | glmnet | mn_log_loss | 0.008 |
| valid | lightgbm | mn_log_loss | 0.008 |
| valid | glmnet | roc_auc | 0.918 |
| valid | lightgbm | roc_auc | 0.948 |
4 Predictions
What new and upcoming games does the model predict for GOBBluth89?
The following table displays the top 15 games published after 2021 with the highest probability of entering the user’s collection.
| Top 15 (Newer) Games for GOBBluth89 | |||||
| Rankings based on predictive model trained on user's collection using games released through 2021 | |||||
| rank | image | game | description | Pr(Own) | Own |
|---|---|---|---|---|---|
| 1 |  |
Unmatched: Brains and Brawn (2023) | Unmatched: Brains and Brawn, the fifth and final Unmatched Marvel set, features some of Marvel's hottest heroes: Spider-Man, Dr. Strange, and She-Hulk. Spidey swings around the battlefield, using his spider-sense to keep him safe. Dr. Strange has, well, the best card names in the game: Behold the Seven Suns of Cinnibus! And She-Hulk won't think twice about throwing the book — or whatever heavy ... | 0.974 | no |
| 2 |  |
Gloomhaven: Second Edition (2024) | Gloomhaven: Second Edition is a revised and elevated version of the award-winning core game of Gloomhaven. This is the culmination of everything Isaac Childres and the growing Cephalofair Games team have learned since the initial release of Gloomhaven, including feedback from the community, playtesters, co-designers, and developers. The world, story, and challenging gameplay are all still the ... | 0.970 | no |
| 3 |  |
The Witcher: Old World (2023) | In The Witcher: Old World, you become a witcher — a professional monster slayer — and immerse yourself in the legendary universe of The Witcher franchise. Set years before the saga of Geralt of Rivia, The Witcher: Old World explores a time when monsters roamed the Continent in greater numbers, creating a constant peril that required the attention of expertly trained monster slayers, known as w... | 0.966 | no |
| 4 |  |
Unmatched: Jurassic Park – Dr. Sattler vs. T. Rex (2022) | In battle, there are no equals. "Dinosaurs eat man… Woman inherits the earth." The greatest predator the world has ever known is closing in on the tenacious Dr. Sattler. Who has the slightest idea what to expect? In Unmatched: Jurassic Park – Dr. Sattler vs. T. Rex, the massive T rex unleashes fearsome attacks and seems unstoppable while Dr. Sattler makes full use of her surroundings and the a... | 0.942 | yes |
| 5 |  |
Earthborne Rangers (2023) | Earthborne Rangers is a customizable, co-operative card game set in the wilderness of the far future. You take on the role of a Ranger, a protector of the mountain valley you call home: a vast wilderness transformed by monumental feats of science and technology devised to save the Earth from destruction long ago. You begin by building a deck that reflects your Ranger's interests, personal hist... | 0.924 | no |
| 6 |  |
Wardens of Wulvengrad (2022) | A cooperative monster hunting boss battler for 1-4 players against AI controlled monsters set in the low fantasy kingdom of Wulvengrad. Each hunter has a unique deck of actions and abilities, with every card being split in 2 - an action which can be played during the hunter's turn, or a reaction which can be played at any time! Will you attack with everything, or hold some back to defend agains... | 0.840 | no |
| 7 |  |
Fire for Light (2023) | The villagers of Summer's End are preparing for the coming of Malwinter — a strange and legendary season with the harshest snows and deadly cold. Take control of a new generation of explorers, the most valued members of Summer's End who go out every day in search of food, materials, or other resources that the village uses to survive: Narii, who believes there's something in the nearby mo... | 0.793 | no |
| 8 |  |
Zon: Cosmic Warfare (2023) | Zon: Cosmic Warfare places you in control of an alien race in a vast political struggle, competing for success with other races. You will explore the Zon cosmos, upgrade your starting deck, and craft spaceships with which to conquer, defend, and fight. There are many different paths you choose to win, so you will need to adapt to any situation that can come your way while exploring the vastness... | 0.718 | no |
| 9 |  |
Die Seehunde (2023) | Die Seehunde is a solitaire nautical wargame set in the last months of World War 2. You, the player, will be in command of a two crew midget submarine Type XXVIIB called “Seehund” (Seal; plural “Seehunde, die”) or simply “Hund” (Hound) by its crews. Equipped with two G7e Torpedoes, the Seehund was designed as a short range commerce raider for deployment in the North Sea. The game play is divid... | 0.696 | no |
| 10 |  |
The Lord of the Rings: The Card Game – Revised Core Set (2022) | Sometimes, in order to truly appreciate a tale, one must first go back to its beginning. Grand adventures and strong fellowships are important and wonderful, but the first step of any journey is just as important as the last. With that in mind, it’s time to return to the beginning of one of the most epic adventures of all… With increased contents and some quality-of-life improvements, this new... | 0.687 | no |
| 11 |  |
Undaunted: Battle of Britain (2023) | The RAF faces the Luftwaffe in this two-player deck-building game of aerial WWII combat. Summer, 1940. The German war machine has rolled through the continent in less than a year, crushing all before it. Britain is all that stands in the way of German victory in Europe. Command the pilots of the battle-tested Luftwaffe who are looking to extinguish all resistance and pave the way to invasion, ... | 0.662 | no |
| 12 |  |
SOE: Lysander (2023) | SOE: Lysander is the first of a new set of low-cost, book-based games in the "Special Missions" series that put you directly into the cockpit. Your mission is as a pilot in Great Britain's most secret aviation unit, "A" Flight of RAF 161 Squadron (Special Duties). You will fly Special Operations Executive (SOE) agents, wireless operators, saboteurs, assassins, political figures, heads of the F... | 0.646 | no |
| 13 |  |
Havoc! The Combat Card Game (2022) | Havoc! The Combat Card Game! is a fast-paced cards-and-dice game of deadly hand-to-hand combat. Set in the era of swords and shields, spears and axes, Players take on the role of Knights, Barbarians, or other fighters locked in a deadly struggle. Players can choose combat scenarios from a range of historical eras, or from fantasy settings. After choosing fighters, weapons, and armor, Players... | 0.618 | no |
| 14 |  |
Gathering Gloom (2023) | The Charming family is an eclectic family that lives in a manor on top of the hill in the town of Banebridge somewhere in New England circa 1932. They own the local mortuary as well as a mining company. All they want to do is live in peace, take care of their ancestral home, run their businesses, and get along with the townsfolk. The villagers of Banebridge, however, see it differently. Man... | 0.614 | no |
| 15 |  |
Unmatched: Houdini vs. The Genie (2022) | Unmatched is a highly asymmetrical miniature fighting game for two or four players. Each hero is represented by a unique deck designed to evoke their style and legend. Tactical movement and no-luck combat resolution create a unique play experience that rewards expertise, but just when you've mastered one set, new heroes arrive to provide all new match-ups. Unmatched: Houdini vs. The Genie adds ... | 0.560 | no |
4.1 Explaining Individual Predictions
Why did the model predict these games?
4.2 Upcoming Games
Finally, I can examine predictions for all newer and upcoming games.